It's not that Pluto "stopped being" a planet exactly, but rather that astronomers in 2006 decided to change the rules of the game. The thing is, when they discovered other objects similar to Pluto floating around out there in outer space, they realized they needed a stricter definition so they wouldn't end up with 50 different "planets."
The new definition says that a planet has to orbit the sun, be big enough that its own gravity makes it round, and most importantly: it has to have "cleared" its orbit, meaning there aren't other objects of similar size orbiting around there. Pluto meets the first two requirements but fails the third because it shares its orbital space with a bunch of icy debris. That's why it's now a "dwarf planet" instead of a real planet.
You can explain it to your son like this: imagine if at school they decided that to be considered part of a certain group you had to meet three requirements, and it turns out Pluto only ever met two of them. It's not that Pluto changed, it's the definition of what counts as a planet that changed.